Cut a few slices from the onion and place into bottom of pressure cooker, making sure to separate the onion rings. Pour in wine and half of the marinara sauce.
Into the bowl of a food processor, add the rest of the onion, heavy cream, egg, pork rinds, garlic, oregano, basil, salt and pepper and process until well combined, scraping down the sides half way through.
Add ground beef/pork to food processor and pulse in 5 second intervals (about 3-4 times), until combined.
Divide mixture into 16 pieces. Add 1/3 ounce of cheese cubes (3-5 pieces) (really stuff the meatballs) to the middle of each piece and roll into a tight ball and make sure it is completely sealed.
Pour half the sauce into cooking pot and then add meatballs and cover with the rest of the sauce.
Lock on lid and close pressure valve. Cook at high pressure for 5 minutes. When beep sounds, wait 10 minutes and then release the rest of the pressure.
Remove lid and gently stir in Parmesan/Asiago cheese and fresh basil.